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Math Help - Solving Equations using Logs

  1. #1
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    Unhappy Solving Equations using Logs

    I have been set a question f = (uv)/(u+v) I have to solve for v using logarithms. I had done several examples and am confident but not one in this format. Can any one help with a stage by stage how to do? I can do a lot more that seem more complicated but I miss small things sometimes that make the difference. Thanks loads and hope to hear from someone who can put my mind at rest.
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  2. #2
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    Re: Solving Equations using Logs

    So you need to find v in terms of u and f, and you have to use logarithms? That's a very strange problem, is this a homework problem or text book problem where you can state the actual problem?

    YOu can take natural log of both sides:

    ln(f)=ln\right(\frac{uv}{u+v}\left

    and on the right side use the rules of logarithms to expand, and then try to isolate v.

    ln(xy)=ln(x)+ln(y)

    \ln (\right\frac{x}{y}\left)=ln(x)-ln(y)

    e^{ln(x)}=x.
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  3. #3
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    Re: Solving Equations using Logs

    Adkin's jr's "laws of logarithms" are correct but unfortunately there is no "law of logarithms that will allow you to simplify log(u+ v).

    There is simply no reason to use logarithms to solve this equation- it isn't necessary and it doesn't work!

    Instead, if f= uv/(u+ v) then f(u+ v)= fu+ fv= uv so that uv- fv= (u- f)v= fu and then v= fu/(u- f).
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  4. #4
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    Re: Solving Equations using Logs

    Thank you very much. If I am completely honest this equation was not 100% clear it had to be solved using logs. Although my assignment had nothing but log and natural logs which left me confused.
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  5. #5
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    Re: Solving Equations using Logs

    Hi again..thanks for your help I have

    (3.4)^2x+3=8.5 for x

    I got as far as

    (3.4)2x+3=8.5
    (2x+3)log(3.4) = log(8.5)
    (2x+3)x0.531 = 0.929
    (2x+3)x1.062 = 0.929

    then got stuck. The nearest I have got to an answer of 8.5 was 0.87. Out by an order of magnitude!!!
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  6. #6
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    Re: Solving Equations using Logs

    Hi again..thanks for your help I have

    (3.4)^2x+3=8.5 for x

    I got as far as

    (3.4)2x+3=8.5
    (2x+3)log(3.4) = log(8.5)
    (2x+3)x0.531 = 0.929
    (2x+3)x1.062 = 0.929

    then got stuck. The nearest I have got to an answer of 8.5 was 0.87. Out by an order of magnitude!!!
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